a(n) = (n+1) a(n-1) + (-1)^n.

Terms

a(0) =0a(1) =1a(2) =3a(3) =16a(4) =95a(5) =666a(6) =5327a(7) =47944a(8) =479439a(9) =5273830a(10) =63285959a(11) =822717468a(12) =11518044551a(13) =172770668266